Question

3 multiple choice 1 point decide whether each set of numbers is a triangle. 5,10,15 yes no 4 multiple choice 1 point decide whether each set of numbers is a triangle. 6,9,16 yes no

Explanation:

Step1: Recall triangle - inequality theorem

For three side - lengths \(a\), \(b\), and \(c\) of a triangle, the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check the set \(5,10,15\)

We have \(5 + 10=15\), but for a triangle \(a + b>c\) must hold for all combinations of side - lengths. Since \(5 + 10\) is not greater than \(15\), this is not a triangle.

Step3: Check the set \(6,9,16\)

Calculate \(6+9 = 15<16\). Since \(6 + 9\) is not greater than \(16\), this is not a triangle.

Answer:

1. B. No
2. B. No